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By Matt Siegel

SYDNEY (Reuters) - A 29-year-old Frenchman shouted "Allahu Akbar" (God is Greatest) as he stabbed a British woman to death and wounded two people at a backpackers' hotel in Australia, police said on Wednesday.

The man was in Australia on a valid tourist visa and had no known links to radical groups such as Islamic State, which has urged its followers to carry out attacks with knives or other readily available weapons, police said.

British and Australian media identified the dead woman as Mia Ayliffe-Chung, 21, from the English county of Derbyshire. The Australian Broadcasting Corp said that she was in the country on a working holiday.

A 30-year-old British man was in critical condition in hospital after the late Tuesday attack in Queensland state, south of the city of Townsville.

Police said they were not ruling out any motive.

"Initial inquiries indicate that comments which may be construed of being of an extremist nature were made by the alleged offender," Queensland Police Service Deputy Commissioner Steve Gollschewski told reporters.

"This person appears to have acted alone," he said. "He is a visitor to Australia and has no known local connections, however investigations are ongoing."

Australia, a staunch U.S. ally, has been on heightened alert for attacks by home-grown Islamist radicals since 2014 and authorities say they have thwarted a number of plots.

About 100 people have left Australia for Syria to fight alongside organisations such as Islamic State, Australia's Immigration Minister said this year.

The FBI on Tuesday said it was investigating a similar attack in Virginia, in which a suspect shouted the same words while attacking a man and woman with a knife. Similar attacks have recently occurred in France, Bangladesh and Germany.

There have been several "lone wolf" assaults in Australia, including a 2014 cafe siege in Sydney that left two hostages and the gunman dead. Also in 2014, police shot dead a Melbourne teenager after he stabbed two counter-terrorism officers.

In 2015, a 15-year-old boy fired on an accountant at a police headquarters in a Sydney suburb and was killed in a gunfight with police.

Police did not give details of the third person wounded in the attack, which was captured on video and witnessed by more than a dozen people. There was no ongoing threat to the community, Gollschewski said.